JEE Main 2018MathematicsBinomial TheoremHardMCQ

JEE Main 2018 — Binomial Theorem Question with Solution

JEE Main 2018 (15 Apr)

Question

If n is the degree of the polynomial, 25x3+1-5x3-18+ 25x3+1+5x3-18 and m is the coefficient of xn in it, then the ordered pair n, m is equal to

Choose an option

Show full solutionCorrect option: C
Correct answer
C12, 204

Step-by-step explanation

25x3+1-5x3-18+ 25x3+1+5x3-18

Rationalizing denominators of both the brackets,

=5x3+1+ 5x3-1  8+ 5x3+1 - 5x3-1  8

=28C0 5x3+18+8C25x3+165x3-12+8C45x3+145x3-14+8C65x3+125x3-16+8C85x3-18

=25x3-14+285x3+135x3-1+705x3+125x3-12+285x3+15x3-13+5x3+14

So, n=12 and 

m=254+140.53+70.54+140.53+54=160000=204

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About this question

This is a previous-year question from JEE Main 2018, covering the Binomial Theorem chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.